论文标题
罗森塔尔的空间被重新审视
Rosenthal's space revisited
论文作者
论文摘要
令$ e $为$ [0,1] $上的重新安排不变性（r.i。）功能空间，让$ z_e $由$（0，\ infty）$上的所有可测量函数$ f $组成，使得$ f^*χ_ {[0,1] [0,1]} \ in e $和$ f^*χ_ $ _ $ f^$ n l^$ n l^[1，}}。我们揭示了对应于空间$ z_e $的广义Rosenthal空间的属性之间的密切连接，以及在$ e $中的独立对称分布式随机变量的行为。获得的结果用于考虑$ [0,1] $和$（0，\ infty）$之间存在的同构的问题。利用了不相交序列的特定属性，我们确定了$ [0,1] $`close''上的一类新的R.I. \ Space，to $ l^\ infty $，这对R.I. \ spaces in $（0，\ infty）$均未是同构。特别是，该属性由lorentz空间$λ_2（\ log^{ - α}（e/u））$共享，其中$ 0 <α\ le 1 $。
Let $E$ be a rearrangement invariant (r.i.) function space on $[0,1]$, and let $Z_E$ consist of all measurable functions $f$ on $(0,\infty)$ such that $f^*χ_{[0,1]}\in E$ and $f^*χ_{[1,\infty)}\in L^2$. We reveal close connections between properties of the generalized Rosenthal's space, corresponding to the space $Z_E$, and the behaviour of independent symmetrically distributed random variables in $E$. The results obtained are applied to consider the problem of the existence of isomorphisms between r.i.\ spaces on $[0,1]$ and $(0,\infty)$. Exploiting particular properties of disjoint sequences, we identify a rather wide new class of r.i.\ spaces on $[0,1]$ ``close'' to $L^\infty$, which fail to be isomorphic to r.i.\ spaces on $(0,\infty)$. In particular, this property is shared by the Lorentz spaces $Λ_2(\log^{-α}(e/u))$, with $0<α\le 1$.
